**Introduction Study Graphing Expression:**

**Study graphing expression is to study the graphing method on how to graph the given values. The graphing expression method to draw a graph based on the x and y values. The coordinate values are from the any type of graphic shape the x values plot in the x axis and y values plot in the y axis.The graph represents the relationship between this two coordinates.**

**Study graphing expression explanation:**

Two variables x and y are linked by an equation of the form y = ax2 + bx + c then it is called a quadratic polynomial. We have already seen in Algebra that the equation ax2 + bx + c = 0 is a quadratic equation. This is the reason why we call y = ax2 + bx + c as a quadratic graph. For each value of x the equation y = ax2 + b x + c gives a value of y and we obtain an ordered pair (x, y) of real numbers. The set of all such ordered pairs define the graph of y = ax2 + bx + c called the quadratic graph.

The following method is used in drawing quadratic graphs:

By alternate selected values for x in the equation y = ax2 + bx + c, we get corresponding values for y and then we form a table.

Draw x-axis and y-axis on the graph sheet and choose a suitable scale on the co-ordinates axes.

The scale for both the axes is chosen depending on the values of the co-ordinates obtained.

Plot the points in the Cartesian plane of the graph sheet.

Join these points by a smooth curve, then we get the required quadratic graph of y = ax2 + bx + c.

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Study graphing expression with example problem:

Draw the graph of y = x3

**Solution:**

Draw x-axis and y-axis on the graph sheet. Mark the scales on x-axis 1 cm = 1 unit

And on y-axis 1 cm = 3 units. Assign values for x = – 2 to 3 and we get the corresponding y Values tabulated as follows:

x : –2 –1 0 1 2 3

y = x3: -8 - 1 0 1 8 27

Plot the points (–2,-8), (–1,-1), (0, 0), (1, 1), (2, 8), (3, 27) on the graph sheet and join the points by smooth curve. This curve is called the parabola y = x³